Comment on ‘‘Capillary Filling of Anodized Alumina Nanopore Arrays’’ A recent Letter [1] presents a study of adsorption- desorption of perfluoromethylcyclohexane (PFMC) in an array of cylindrical pores in Al2O3. A hysteretic transition

A recent Letter [1] presents a study of adsorptiondesorption of perfluoromethylcyclohexane (PFMC) in an array of cylindrical pores in Al2O3. A hysteretic transition is observed. It is argued that its width (0.4 K) is 5 times smaller than the prediction by Cohan [2] (1.9 K) and that the data agree better with the Cole-Saam theory (CST) [3,4], which includes interactions with the pore walls. By carrying the comparison to its full extent, this Comment questions some conclusions of Ref. [1]. Adsorption is usually measured at constant temperature T by increasing the pressure P of a vapor from 0 to the saturated vapor pressure Psat T . The CST calculates the liquid volume fraction V as a function of p P=Psat T . Alvine et al. measure V as a function of the temperature offset T between the porous sample at Ts and a liquid PFMC reservoir at Tr. They find that the volume fractions at the onset of filling (Vc) and the completion of emptying (Vm) compare well with the CST, but they explain that, in CST, ‘‘there is no prediction of the T where the desorption transition initiates [ Tm], and it is not possible to translate Vc and Vm into a hysteresis width.’’ We shall see that the CST does provide a relation between V and T, which disagrees with the data. Before that, we criticize the calculation of adsorption made in Ref. [1] within a Derjaguin approximation to the CST: the film thickness d before filling is assumed small compared to the pore radius R, leading to Eq. (7) of Ref. [1]. The solid curve in Fig. 3 of Ref. [1] gives the impression of describing well the filling, including the experimental filling temperature T c 1:9 K. However, our calculation for R 11:8 nm (used in Ref. [1]) produces a different curve, with Tc 2:7 K and d 2:8 nm at filling (instead of 3.3 nm [1]). To find T c requires R 16 nm, out of the range of electron microscopy measurements (10:5 2:5 nm) [1]. We now turn to the comparison with the full CST (without assuming d R). In Ref. [1], Tr sets the vapor pressure at Psat Tr . As Ts goes down to Tr, p Psat Tr =Psat Ts increases up to 1, and V p can be converted into V T , using T NAkBT r =Hvap lnp, with Hvap 33:9 kJmol 1 [1]. As T=Tr is a few percent, we ignore the T dependence of other parameters. If the pores all have the same R 11:8 nm, the full CST predicts Tc 2:8 K, Vc 0:43, Tm 4:5 K, and Vm 0:22 (Fig. 1). The CST does not agree better with the data than the Cohan theory. To reproduce T c , one must change R or the Hamaker constant A for PFMC on Al2O3. R 16:2 nm gives Tc 1:9 K, Vc 0:38, Vm 0:18, but Tm 3:2 K remains too high; anyhow, R cannot be that large. Going back to R 11:8 nm, Tc depends weakly on A: one needs to divide A by 104 to find T c , but Vc 0:05 and Vm 0:01 are then too low and Tm 3:8 K too high. Alvine et al. also note that ‘‘the desorption transition occurs at lower T than either prediction’’ and ‘‘while some of the shift may be due to broadening of the transition by pore diameter polydispersity, this effect seems insufficient to fully account for the shift.’’ Following [4], where the CST was compared with helium data, we have tried a Gaussian distribution: the transitions broaden but remain centered on the same T (Fig. 1). The CST does not give a satisfactory account of the results, not only for desorption, as stated in Ref. [1], but also for adsorption. Complete wetting has been assumed. If wetting is only partial with a contact angle , Tm is lowered [2]. The hysteresis width is multiplied by 2 cos 1; 53 would fit the experiment. It would be interesting to measure . To improve the theoretical description, one may use simulations or density functional theory [5]. The existence of a hysteresis critical temperature Tch, at which hysteresis vanishes [6], could also be relevant. From the ratio between the molecular diameter of PFMC and R, we estimate Tch ’ 430 K, and Tr=Tch ’ 0:71.